初等函数教学中的几个问题

Problems in Primary Functions Teaching

本文对比较特殊的两类初等函数——幂指函数与分段函数的初等性加以研究。对于幂指函数,首先利用对数恒等式说明其初等性,再用初等函数的求导法则求出其导数;对于分段函数,则由最常见的函数y=x的初等性展开联想,得到一类连续的分段函数的初等性。为避免混淆,还举例说明:并非所有连续的分段函数都是初等函数。

This article mainly discusses the primary characteristics of the two kinds of special functions: division function and power - exponential function. After analyzing some examples, it points out that some continuous division functions aren’t primary function.